<PAGE>
 
================================================================================

                                   FORM 10-Q
                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549

                      ----------------------------------

(Mark One)
 
[X]  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
     ACT OF 1934
 
     For the quarter ended March 31, 1998
 
                                      OR
 
[ ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
     EXCHANGE ACT OF 1934
 
     For the transition period from __________________ to __________________
     Commission file number 1-10877


                         TERRA NITROGEN COMPANY, L.P.
            (Exact name of registrant as specified in its charter)


                 Delaware                                73-1389684
     (State or other jurisdiction of        (I.R.S. Employer Identification No.)
      incorporation or organization)


              Terra Centre
     PO Box 6000, 600 Fourth Street
            Sioux City, Iowa                             51102-6000
 (Address of principal executive office)                 (Zip Code)


                        Registrant's telephone number:
                                (712) 277-1340

                                        

     At the close of business on April 30, 1998, there were 18,501,576 Common
Units outstanding.


     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.
 X   Yes   ___ No
---              

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                                       1
<PAGE>

                         PART I. FINANCIAL INFORMATION
Item 1. Financial Statements
                         TERRA NITROGEN COMPANY, L.P.
                          CONSOLIDATED BALANCE SHEETS
                                (In Thousands)
<TABLE> 
<CAPTION> 
                                                                 March 31,    December 31,    March 31,
                                                                   1998           1997          1997
                                                                 ---------    ------------    ---------
                                                                (Unaudited)                  (Unaudited)
<S>                                                              <C>          <C>             <C> 
Assets
  Current assets:
     Cash and cash equivalents                                   $  1,535        $ 31,268      $ 61,371
     Accounts receivable                                            2,389           4,007           581
     Inventory - finished products                                 31,586          19,241        30,849
     Inventory - materials and supplies                            15,287          11,437        17,511
     Prepaid expenses and other current assets                      2,961           2,311         2,723
                                                                 --------        --------      --------
  Total current assets                                             53,758          68,264       113,035

  Net property, plant and equipment                               169,073         169,533       171,378

  Other assets                                                     11,925          16,031        19,387
                                                                 --------        --------      --------
   Total assets                                                  $234,756        $253,828      $303,800
                                                                 ========        ========      ========

Liabilities and partners' capital


  Current liabilities:
    Accounts payable and accrued liabilities                     $ 27,043        $ 26,524      $ 48,533
    Customer prepayments                                            4,306           4,746        11,335
    Current portion of long-term debt and
     capital lease obligations                                      1,083           1,070         1,036
                                                                 --------        --------      --------
  Total current liabilities                                        32,432          32,340        60,904

  Long-term debt and capital lease obligations                      8,770           8,966         2,869
  Long-term payable to affiliates                                   4,996           4,687         3,845
  Other long-term obligations                                       1,060           1,060         1,060
  Partners' capital                                               187,498         206,775       235,122
                                                                 --------        --------      --------
   Total liabilities and partners' capital                       $234,756        $253,828      $303,800
                                                                 ========        ========      ========
</TABLE> 

See accompanying notes.

                                       2
<PAGE>
 
                         TERRA NITROGEN COMPANY, L.P.
                       CONSOLIDATED STATEMENTS OF INCOME
                                  (Unaudited)
                    (In Thousands, Except Per Unit Amounts)

<TABLE>
<CAPTION>
                                                           Three Months Ended
                                                          ---------------------
                                                                March 31,
                                                           1998          1997
                                                          -------       -------
<S>                                                       <C>           <C> 
Revenues                                                  $48,499       $74,045
Other income                                                  417           134
                                                          -------       -------
Total revenues                                             48,916        74,179

Cost of goods sold                                         40,595        42,509
                                                          -------       -------

Gross profit                                                8,321        31,670
Operating expenses                                          2,443         2,970
                                                          -------       -------

Operating income                                            5,878        28,700

Interest expense                                             (491)         (434)
Interest income                                               414         1,526
                                                          -------       -------

Net income                                                $ 5,801       $29,792
                                                          =======       =======

Net income allocable to
 limited partners' interest                               $ 5,685       $27,175
                                                          =======       =======

Net income per limited
 partnership unit                                         $  0.31       $  1.44
                                                          =======       =======

</TABLE>

See accompanying notes.

                                       3
<PAGE>
 
                         TERRA NITROGEN COMPANY, L.P.
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                  (Unaudited)
                                (In Thousands)
<TABLE> 
<CAPTION> 
                                                                        Three Months Ended
                                                                             March 31,
                                                                      ------------------------
                                                                        1998            1997
                                                                      --------        --------
<S>                                                                   <C>             <C> 
Operating activities:

   Net income                                                         $  5,801        $ 29,792
   Adjustments to reconcile net income to net cash      
    provided by operating activities:
       Depreciation and amortization                                     3,045           2,948
       Changes in operating assets and liabilities:     
       
         Receivables                                                     1,618          10,473
         Inventories                                                   (16,195)        (18,662)
         Prepaid expenses                                                 (650)           (370)
         Accounts payable, accrued liabilities and
           customer prepayments                                             79         (20,756)
       Change in other assets                                            4,106           6,163
       Other                                                               311              74
                                                                      --------        --------
Net cash provided by (used in) operating activities                     (1,885)          9,662

Net cash used in investing activities:

       Capital expenditures                                             (2,587)         (1,628)

Financing activities:

       Proceeds from elimination of distribution reserve fund                -          18,480
       Repayment of long-term debt and capital lease obligations          (183)           (293)
       Partnership distributions                                       (25,078)        (11,612)
                                                                      --------        --------
Net cash provided by (used in) financing activities                    (25,261)          6,575
                                                                      --------        --------
Net increase (decrease) in cash and cash equivalents                   (29,733)         14,609
Cash and cash equivalents at beginning of period                        31,268          46,762
                                                                      --------        --------
Cash and cash equivalents at end of period                            $  1,535        $ 61,371
                                                                      ========        ========
</TABLE> 
See accompanying notes.

                                       4
<PAGE>
 
                         TERRA NITROGEN COMPANY, L.P.
                                        
            Notes to Consolidated Financial Statements (Unaudited)


1.   Basis of Presentation

     The consolidated financial statements contained herein should be read in
conjunction with the consolidated financial statements and notes thereto
contained in the Terra Nitrogen Company, L.P. ("TNCLP") Annual Report on Form 
10-K for the year ended December 31, 1997. TNCLP and its operating partnership
subsidiary, Terra Nitrogen, Limited Partnership (the "Operating Partnership"),
are referred to herein, collectively, as the "Partnership".

     The accompanying unaudited consolidated financial statements reflect all
adjustments which are, in the opinion of management, necessary for the fair
statement of the results for the periods presented. All of these adjustments are
of a normal and recurring nature. Results for the quarter are not necessarily
indicative of future financial results of the Partnership.

     Net income per limited partnership unit is computed by dividing net income,
less a 2% and 9% share allocable to the General Partner for the three months
ended March 31, 1998 and 1997, respectively, by 18,501,576 and 18,808,778
limited partner units for the 1998 and 1997 periods, respectively. The net
income allocated to the General Partner decreased to 2% during the three months
ended March 31, 1998 as there was no Available Cash to distribute for the first
quarter of 1998. According to the Agreement of Limited Partnership of TNCLP, net
income is allocated to the General Partner and the Limited Partners in each
taxable year in the same proportion as Available Cash for such taxable year was
distributed to the General Partner and the Limited Partners. If there is no cash
distribution, net income or loss is allocated to the Limited Partners and the
General Partner based on their respective ownership percentages. Distributions
of Available Cash are made 98% to the Limited Partners and 2% to the General
Partner, except that the General Partner is entitled, as an incentive, to larger
percentage interests (up to 50%) to the extent that distributions of Available
Cash exceed specified target levels. Available Cash for the three months ended
March 31, 1998 decreased $20.9 million from the three months ended March 31,
1997 due primarily to lower net income in 1998 partially offset by lower working
capital requirements in the 1998 quarter. In addition, 1997 Available Cash
included $18.5 million from the elimination of the Reserve Amount during 1997
(see Note 2).

2.   Distributions to Unitholders

     The Partnership makes quarterly cash distributions to Unitholders and the
General Partner in an amount equal to 100% of its Available Cash (as this and
other capitalized terms are defined in the Partnership Agreement).


                                       5
<PAGE>
 
     The quarterly cash distributions paid to the Units and to the General
Partner applicable to 1998 and 1997 were as follows:

<TABLE>
<CAPTION>
                       Senior Preference Units           Common Units                General Partner
                      -------------------------    -------------------------    -------------------------
                      Total (000s)   $ Per Unit    Total (000s)   $ Per Unit    Total (000s)   $ Per Unit
                      ------------   ----------    ------------   ----------    ------------   ----------

<S>                   <C>            <C>           <C>            <C>           <C>            <C>
1998:
  First Quarter            $-           $-           $21,647        $ 1.17         $ 3,431         $-


1997:
  First Quarter            186          .605          27,752          1.50          10,477          -
  Second Quarter           186          .605          18,871          1.02           1,836          -
  Third Quarter             -             -           44,034          2.38          26,686          -
  Fourth Quarter            -             -            5,366           .29             109          -
</TABLE>

     The distributions paid in the first and second quarters of 1997 to the
holders of the Senior Preference Units ("SPUs") represented an amount equal to
the minimum quarterly distribution ("MQD") for each quarter. Non-converting SPU
holders were not entitled to participate in cash distributions in excess of the
MQD after December 31, 1996.

     The Reserve Amount of $18.5 million (included in cash and cash equivalents
at March 31, 1997) was distributed out of Available Cash on May 27, 1997 to
holders of the Common Units and to the General Partner. Since the non-converted
SPUs were redeemed on May 27, 1997, the Reserve Amount is no longer required to
be maintained.

3.   Cash and cash equivalents

     The Partnership has a demand deposit with an affiliate that represents
excess Partnership cash deposited with Terra Capital, Inc., the parent of the
General Partner. The deposit is due on demand and at March 31, 1998 the interest
rate was 6.9%. The amount of the demand deposit included in cash and cash
equivalents was $1.5 million at March 31, 1998.

4.   Natural gas costs

     The Partnership's natural gas procurement policy is to effectively fix or
cap the unit cost of 40-80% of its natural gas requirements for the upcoming 12
months and up to 50% of its natural gas requirements for the subsequent two-year
period using supply contracts, financial derivatives and other forward pricing
techniques in an attempt to gain some protection against natural gas price
increases on the spot market. Consequently, if natural gas prices were to
increase in a future period, the Partnership may benefit from these forward
pricing techniques; however, if natural gas prices were to decline, the
Partnership may incur costs above the spot market price as a result of such
policies.

     The settlement dates for such financial instruments are scheduled to
coincide with gas purchases during future periods. These instruments are based
on a designated price, which is referenced to market natural gas


                                       6
<PAGE>
 
prices or appropriate NYMEX futures contract prices. The Partnership frequently
uses prices at the Henry Hub in Louisiana, the most common and financially
liquid location of reference for financial derivatives related to natural gas;
however, natural gas supplies for the Partnership's two production facilities
are purchased from various suppliers at locations that are different from Henry
Hub. This creates a location basis differential between the contract price and
the physical price of natural gas. Accordingly, the use of financial derivatives
may not exactly offset the change in the price of physical gas. The Partnership
uses basis swaps to maintain fixed prices for the location basis differential.

     As of March 31, 1998, the Partnership had effectively fixed or capped the
price of a substantial portion of its natural gas requirements for 1998 and
1999, consistent with its policy mentioned above. Unrealized gains from forward
pricing positions totaled $24.8 million and $9.7 million as of March 31, 1998
and 1997, respectively.

     For the three months ended March 31, 1998, natural gas hedging activities
produced cost savings compared with spot prices of $1.8 million compared with
savings of $9.4 million for the 1997 period.


                                       7
<PAGE>
 
Item 2.  Management's Discussion and Analysis of Financial Condition and Results
of Operations

Results of Operations

Three months ended March 31, 1998, compared with the three months ended March
31, 1997

Volumes and prices for the three-month periods ended March 31, 1998 and 1997
were as follows:

<TABLE>
<CAPTION>
                                  1998                                     1997
                    --------------------------------     ----------------------------------------
                        Sales             Average             Sales                  Average
                       Volumes          Unit Price           Volumes               Unit Price
                      (000 tons)          ($/ton)          (000 tons)                ($/ton)
                    --------------     -------------     ---------------        -----------------

<S>                 <C>                <C>               <C>                    <C>
Ammonia                   63                142                 85                     207
UAN                      390                 63                407                      90
Urea                     137                108                114                     173
</TABLE>

     Revenues for the quarter ended March 31, 1998 declined $25.3 million, or
34%, compared with the same quarter in 1997 due to lower nitrogen prices for all
Partnership products.  Surplus worldwide nitrogen production continued to put
pressure on prices during the 1998 quarter resulting in price reductions of 31%,
30% and 37% for ammonia, UAN and urea, respectively, compared with the 1997
quarter.  Worldwide urea prices have declined due to a lack of purchases by
China, a major purchaser of urea in the world markets. Increased production in
China led to a significant reduction in their urea purchases in world markets
and caused urea prices to decline from prior year levels.

     Ammonia sales volumes declined 26% compared with the prior year quarter
primarily due to wet weather in part of our marketing area during the 1998
quarter.  Urea sales volumes increased 20% from the 1997 quarter due to lower
urea prices, reduced imports into the United States in 1998 and lower dealer
inventories at the beginning of 1998.

     Cost of goods sold as a percentage of revenues increased to 83% for the
1998 quarter from 57% in the 1997 period primarily as a result of lower nitrogen
selling prices as gas costs during the 1998 quarter were slightly below those of
the 1997 quarter.  The Partnership's natural gas forward pricing activities
produced $1.8 million in cost savings during the 1998 period compared with $9.4
million in the 1997 quarter.

     Interest income decreased $1.1 million compared with the 1997 period due to
lower levels of cash and short term investments from lower earnings and due to
the elimination of the Reserve Amount as a result of the redemption of the non-
converted SPUs during the second quarter of 1997.

                                       8
<PAGE>
 
Capital resources and liquidity

     Operating activities for the first three months of 1998 used $1.9 million
in cash compared with the 1997 period which provided $9.7 million in cash.  The
reduction in cash provided by operating activities of $11.5 million was
principally due to lower net income ($24.0 million) partially offset by changes
in working capital which were more favorable in the 1998 quarter compared with
the prior year quarter.  The changes in working capital from operating
activities for the 1998 quarter used cash of $15.1 million compared with the
1997 period which used cash of $29.3 million.  Both the 1998 quarter and the
1997 quarter reflected an increase in inventories of $16.2 million and $18.7
million, respectively, due in part to lower than expected sales volumes and due
to the seasonal buildup of inventories in anticipation of the spring planting
season.  The 1997 quarter reflected an increased use of cash from working
capital changes as a result of lower accounts payable and accrued liabilities
due to lower gas prices at March 31, 1997 compared with December 31, 1996.  The
increased cash usage was partially offset by lower accounts receivable due to
accruals at December 31, 1996 for income on gas hedges received in January 1997
compared with no such accruals at March 31, 1997.

     The Partnership's principal needs for funds are for support of its working
capital, distributions to Partners, and capital expenditures. The Partnership
intends to fund such needs primarily from net cash provided by operating
activities and, to the extent permitted thereunder, from funds available under
the Operating Partnership's revolving credit facility.  At March 31, 1998, the
Operating Partnership had $18 million of unused borrowing capacity under its
revolving credit facility.  The Partnership believes that such sources of funds
will be adequate to meet the Partnership's working capital needs, make quarterly
distributions to Partners and fund the Partnership's capital expenditures for at
least the next twelve months.

     Quarterly distributions to the Partners of TNCLP are based on Available
Cash for the quarter as defined in the Agreement of Limited Partnership of
TNCLP.  Available Cash is defined generally as all cash receipts less all cash
disbursements, adjusted for changes in certain reserves established as the
General Partner determines in its reasonable discretion to be necessary.
Distributions on the Common Units are cumulative to the extent that, for any
calendar quarter, if a distribution of at least $.605 is not paid to the holders
of the Common Units, the amount of the shortfall (plus any arrearages from prior
quarters) will be paid out of Available Cash in subsequent quarters before any
incentive distributions are paid to the General Partner. During the first three
months of 1998, the Partnership paid $25.1 million in distributions to its
Partners.  As of March 31, 1998, there was no distribution arrearage on the
Common Units.

     Available Cash for the three months ended March 31, 1998 was zero, a
decrease of $20.9 million compared with the three months ended March 31, 1997
due primarily to lower net income in 1998 and to higher Available Cash in 1997
due to the elimination of the $18.5 million Reserve Amount.

     Finished products inventory increased $12.3 million from the December 31,
1997 balance primarily due to lower than anticipated UAN sales volumes during
the 1998 quarter and due to the seasonal buildup of inventory in anticipation of
the spring planting season.

     Other assets declined $4.1 million and $7.5 million from the December 31,
1997 and March 31, 1997 balances, respectively, due to the amortization of
deferred turnaround costs during 1997 and 1998.  A scheduled 

                                       9
<PAGE>
 
turnaround was completed at the Blytheville Plant during the third quarter of
1996. Costs related to the periodic scheduled maintenance of production
facilities (plant turnarounds) are capitalized when incurred and amortized on a
straight-line basis until the next scheduled turnaround, generally over one or
two years.
     
     Accounts payable and accrued liabilities declined $21.5 million from the
March 31, 1997 balance principally due to the timing of cash transfers between
the Partnership and its affiliates.

     Customer prepayments declined $7.0 million from the March 31, 1997 balance
due primarily to customer's anticipation of a decline in nitrogen prices during
late 1997 and a delay in purchase decisions until the 1998 spring planting
season.  Certain customers prepay for product during the fall and winter months
to take advantage of generally favorable pricing conditions.  The customers then
take delivery of the product as needed during the spring planting season.

     Long-term debt and capital lease obligations increased $5.9 million from
the March 31, 1997 balance as $7.0 million was borrowed under the revolving
credit facility in the second quarter of 1997 to fund the redemption of the non-
converted SPUs.

Capital expenditures

     Capital expenditures totaled $2.6 million for the first three months of
1998.  For the remainder of 1998, the Partnership plans to spend approximately
$6 million.  Plans for 1998 include urea storage and loading improvements at the
Blytheville plant and environmental control, equipment replacement and
efficiency improvements at both plants.

Environmental matters

     The Partnership is subject to federal, state and local environmental,
health and safety laws and regulations, particularly relating to air and water
quality.  In the course of its ordinary operations, the Partnership has and will
generate wastes which may fall within the definition of "hazardous substances"
under federal or state laws.  The Partnership's production facilities and
storage locations require ongoing operating expenditures in order to remain in
compliance with environmental regulations. These operating costs consist largely
of such items as electrical and chemical usage, waste disposal, laboratory
analysis, fees for outside consultants and contractors, and salaries for
environmental employees.

     Based on its current knowledge, the Partnership does not expect capital
expenditures relating to environmental matters to have a material adverse effect
on its results of operations, financial condition, capital resources, liquidity
or cash flow.  The Partnership does not expect that any further material capital
expenditures will be required to comply with existing environmental regulations.
Based on such regulations, the Partnership does not believe that it will be
required to make any material environmental remediation expenditures in the
foreseeable future.

                                       10
<PAGE>
 
Year 2000 issue

     The Year 2000 issue concerns computer programs that use only the last two
digits to identify the year in date fields.  If not corrected, many of these
computer programs could fail or create erroneous results on or before January 1,
2000.  This issue affects virtually every company.

     The Partnership has assigned dedicated resources to address its Year 2000
issues.  A significant part, but not all, of the Partnership's management
information systems environment has been assessed for Year 2000 issues and
necessary remedial actions have been identified in these assessed areas.  The
impact of these remedial actions for areas where an assessment has already been
completed is not expected to be material.  Remedial actions taken to date have
been completed at minimal cost.

     The Partnership has initiated an additional organization-wide review of all
possible computing functions, including the process control systems and
instrumentation in the manufacturing facilities.  The Partnership is also
assessing Year 2000 issues in relation to its customers, suppliers and other
constituents because the actions or inactions of such third parties may
materially affect the Partnership.

     The Partnership anticipates that it will complete all assessment,
remediation and testing efforts for Year 2000 issues in advance of January 1,
2000 with no material adverse consequences or significant costs to the
Partnership.  However, the costs or consequences of incomplete or untimely
resolution of Year 2000 issues by the Partnership or third parties could have a
material adverse affect on the Partnership.

Limited Call Right


     If at any time not more than 25% of the Common Units are held by non-
affiliates of the General Partner, either TNCLP, the General Partner or its
affiliates may call all such outstanding units held by non-affiliated persons in
accordance with the terms of the TNCLP partnership agreement.  TNCLP is required
to give at least 30 but not more than 60 days notice of its decision to purchase
the outstanding units of the class.  The purchase price per unit is required to
be the greater of (1) the average of the previous twenty trading days closing
prices as of the date five days before the purchase is announced or (2) the
highest price paid by the General Partner or any of its affiliates for any unit
within the 90 days preceding the date the purchase is announced.

     The General Partner and its affiliates own 66.8% of the Common Units as of
April 30, 1998.  Under existing authorization of the board of directors of Terra
Industries Inc., the indirect parent of the General Partner, additional Common
Units may be purchased on the open market and through privately negotiated
transactions by affiliates of the General Partner to bring this ownership level
above 75%.  Although TNCLP and its affiliates reserve the right to consider in
the future whether to acquire all of the Common Units, they do not have any
present plan or intention to do so.

                                       11
<PAGE>
 
                          Part II.  Other Information


Item 6.  Exhibits and Reports on Form 8-K

     (a)  Exhibits:

            10.66  Amended and Restated Credit Agreement dated as of March 31,
                   1998 among Terra Capital, Inc., Terra Nitrogen, Limited
                   Partnership, certain Guarantors, certain Lenders, certain
                   Issuing Banks, NationsBank, N.A., as Syndication Agent, The
                   Chase Manhattan Bank, as Documentation Agent, and Citibank,
                   N.A., as Administrative Bank, filed as Exhibit 4.4 to Terra
                   Industries Inc. Form 10-Q for the period ended March 31, 1998
                   (File No. 1-8520), is incorporated herein by reference.

            10.67  1998 Incentive Award Program for Officers and Key Employees,
                   filed as Exhibit 10.1.16 to Terra Industries Inc. Form 10-Q
                   for the period ended March 31, 1998 (File No. 1-8520), is
                   incorporated herein by reference.

            27     Financial Data Schedule. (EDGAR  only)

     (b)  Reports on Form 8-K:
 
                   Current Report on Form 8-K dated April 23, 1998 reporting
                   first quarter results, declaring no distribution and
                   projecting certain future distributions.
 
                                      12
<PAGE>
 
                                   SIGNATURE


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                       TERRA NITROGEN COMPANY, L.P.

                                   By: TERRA NITROGEN CORPORATION
                                       as General Partner


                                   By: /s/ Erik L. Slockers
                                       --------------------------------------
                                       Erik L. Slockers
                                       Vice President, Controller
                                       (Principal Accounting Officer)


Date: May 14, 1998

                                      13